Phase Equilibria in Hydrocarbon Systems V. Pressure-Volume-Temperature Relations and Thermal Properties of Propane' BRUCEH. SAGE,J. G. SCHAAFSMA, AND WILLIAM N. LACEY California Institute of Technology, Pasadena, Calif.
I
N THE study of simple multicomponent systems it is
desirable to know the pressure-volume-temperature relations and the thermal properties of each of the components over the pressure and temperature range through which the more complex system is studied. Published data on propane, one of the important components of ind u s t r i a l hydrocarbon syst e m s , a r e f e w ; they are limited to the properties of the s a t u r a t e d l i q u i d and s a t u r a t e d gas at temperatures below 125' F. (2) and to some divergent values of the vapor p r e s s u r e (2, 3) and critical p r e s s u r e a n d temperature ( I ) . The thermal properties which have already been- determined are the heat of vaporization and specific heat under s a t u r a tion conditions up to about 90" F. ( 2 ) and the specific heat at a constant pressure of one a t m o s p h e r e and at temperatures up to the boiling point of water (7). The lack of published data for either the condensed or the superheated region made desirable a rather extended study of the properties of propane from FIGURE1. VARIABLE- atmospheric p r e s VOLUME CELL sure to 3000 pounds per square inch and at temperatures from 70" to 220" F.
the thermal properties of the system as functions of the temperature. Data obtained with the apparatus previously described (8) are not entirely suited for thermodynamic calculations. The cell used was characterized by a constant volume, the pressure being changed at constant temperature by varying the amount of material in the system with resulting changes in composition. The thermodynamic calculations discussed here are applicable only to systems of fixed composition, and much interpolation would be necessary to convert the results from the constant-volume apparatus to the requisite basis. Furthermore, the apparatus was not suitable for studies of the behavior of condensed systems. A new variable-volume cell was designed and constructed to study any sample of a hydrocarbon mixture of constant mass and composition. A diagram of the apparatus is shown in Figure 1. The steel pressure cell, A , had an inside diameter of 2 inches and an inside height of 11 inches. The volume of the cell OCcupied by the hydrocarbon mixture could be varied by addition or withdrawal of mercury through a valve located at B near the bottom of the cell. The mercury was supplied to the apparatus from a steam-driven reciprocating pump a t pressures up to 3500 pounds per square inch. The mercury before being admitted to the cell was preheated t o the temperature of the apparatus. The volume of the space above the surface of the mercury was determined from the position of the mercury surface. This was ascertained by means of an electrical contact, E, mounted upon a hollow rod which entered the bottom of the cell through a packing gland. The wire from contact E was brought out of the cell through the hollow rod and was connected through a sensitive relay to a signal light. The lower threaded portion of the rod, C, engaged a nut, D, which was in turn driven by a worm, F. A small motor attached to F permitted
MITHOD,APPARATUS, AND MATERIALS After experimental determination of the pressure-volume-temperature r e l a t i o n s of a given system, fundamental thermodynamic equations may be rigorously used to calculate the changes in the thermal properties of the system for any isothermal change of state. I n order, however, to follow the changes in thermal properties of the system when changes in temperature are involved, it is necessary to determine the change in a t least one thermal property as a function of temperature while either the volume of the system, the pressure, or some other variable is held constant. This additional experimental information permits the correlation of all 1 Part I appeared on pages 103-6, January, 1934; Part 11, pages 214-17, February, 1934; Part 111, p8ges 652-4, June, 1934; Part IT,pages 874-7, August, 1934.
3
GRAVITY ISOT~ERMS FOR PROPANE FIGURE2. SPECIFIC 1218
November, 1934
-
INDUSTRIAL AND ENGINEERING CHEMISTRY
contact E to be moved up or down the length of cell A . The final adjustment of the position of contact E was made by manual movement of worm F. As rod C was threaded with extreme care, a counter, mounted upon worm F , gave a direct indication of the position of the mercury surface. The total volume over the mercury surface for a given counter reading was determined by adding a known volume of liquid t? the cell and determining the counter reading when the cell was just full of liquid a t atmosrheric pressure. This was indicated by a rapid rise in pressure or a small addition of mercury. The curve of pressure us. counter reading wa8 extrapolated to atmospheric pressure and permitted the determination of the counter reading for a known volume of the cell. The extrapolation to atmospheric pressure was necessary because the density of the calibrating oil was known only a t that pressure. Since the cell was carefully ma-
1219
was connected to the cage by a pair of bevel gears not shown in Figure 1. The addition of this agitator did not affect the uniformity of change in volume of the cell with variations in the height of mercury, as the rods were of uniform diameter and the volume of the ring at the top of the rods was taken into account in the calibrationThe too of the cell was removable to allow the addition of nonvolatile liquids. Because of the use of a special thin copper gasket, any change in volume of the cell due to removal and replacement of the head was negligible. Volatile pure liquids could be distilled into the cell from weighed pressure containers through valve M . Measured volumes of gas could be admitted through valve N which was connected to the rest of the apparatus (8). The effect of pressure upon the calibration of the apparatus was determined by maintaining the mercury surface a t a fixed osi tion as indicated by a fixed electrical contact in the top orthe cell (not shown in Figure 1) and notin the change in counter reading as the gas pressure over the surface of the mercury was increased from atmospheric to 3000 pounds per square inch. It was found that the maximum pressure correction was less than 0.05 per cent a t the minimum volume of the apparatus. The effect of temperature upon the calibration of the apparatus was taken into account by calibration a t a series of temperatures.
After the variable-volume cell had been constructed and was found to yield such satisfactory pressure-volume-temperature data in the condensed region, it also offered the possibility of an admirable apparatus to determine the specific heats of materials in the condensed region. This could be done by measuring the changes in temperature due to sdiabatic changes in pressure (6).
550
600
PRESSURE
650
700
750
POUNDS PER SQUARE I N C H
FIGURE3. SPECIFICGRAVITYISOTHERMS NEAR THE CRITICAL REGION chined'and the screw was made with high precision (maximum deviation, 0.0004 inch in a length of 11 inches), the volume of the cell for any other counter reading could be reirdily computed. It was found that the osition of the mercury surface could be determined with an aEsolute accuracy of 0.0004 inch, corresponding to a volume of 0.0012 cubic inch (0.021 ml.). The pressure existing in the cell was measured by means of calibrated fluid-pressure scales. One scale had a range from atmospheric to 3000 pounds per square inch and the other from atmospheric to 300 pounds. The reproducible accuracy of each was 1.0 and 0.10 pound per square inch, respectively. They were connected to the bottom of the cell by means of a mercury oil trap (8), suitable corrections being made for the head of mercury in the cell. The temperature of the cell was controlled by an electric heater wound directly on the outside of the cell. In order to maintain constant temperature, a mercury regulator, G (Figure l), was built directly into the wall of the cell. This regulator was connected through a relay to the heater. An auxiliary heater was provided to heat the top of the cell and keep it also a t the desired temperature. A cooling coil wound on the cell permitted studies below room temperature. The cell and its top were insulated from their surroundings by a 1.5-inch layer of ma nesia insulation. Great care was taken in the distribution of t f e heater and in the application of the insulation to insure constant temperature at all points inside of the cell. The temperature of the cell was determined by a calibrated thermometer placed in a deep well in the wall of the cell. That uniformity of the temperature throughout the cell was obtained was shown by the consistency of the dew point of B pure substance a t various total volumes of the apparatus. It is believed that the maximum temperature variation throughout the interior of the cell was about 0.2' F. However, as most of the work was done in a restricted region near the top of the cell, the temperature variations encountered were much less than that. To secure equilibrium, the contents of the cell were agitated by a cage of four vertical rods, H , which was rotated a t about 120 revolutions per minute by the shaft and pulley, K. This shaft
I 100
I 200 PRESSURE
I I I I 400 500 600 P O U N D S PER S Q U A R E I N C H
300
FIGURE4. VAPORPRESSURE OF PROPANE In order to measure the change in temperature, a four-junction copper-constantan thermocouple was installed on the lower surface of the head of the cell. One set of junctions was mounted u on two small Bakelite posts about 0.75 inch below the head orthe cell, while the other junctions were mounted in small glass bulbs (0.0625 inch in diameter) which were inset about 0.125 inch in the wall of the steel head. The adiabatic change in pressure was accomplished by connecting the mercury in the cell to an air chamber of sufficient size so that the pressure in the tube remained constant in spite of the slight leakage past the plunger of the connected fluid-pressure scale. Another air chamber was p d e d which was maintained a t a somewhat different pressure rom that of the first. The pressure in the tube could then be changed easily and rapidly by closing the valve to the first air chamber and opening that to the second. The change gfessure was directly measured on the fluid-pressure scale. igh-
2
1220
INDUSTRIAL AND ENGINEERING CHEMISTRY Vol. 26, No. 11 TABLEI. PHYSICAL AND THERMAL PROPERTIES OF PROPANE AS SUPERHEATED GASAND CONDENSED LIQUID
-70'
4.997 2.417 1.552 1.113 0.841
f/P 0.9731 0.9435 0.9149 0.8855 0.8559
:...
0.5509
U
PO
25 50 75 100 125 150 175 200 225 250 275 300 350 400 450 500 550 600 700 800 900 1000 1250 1500 1750 2000 2250 2500 2750 3000
...
.... ....
0 03 174
....
...
0.4518
....
0:03159
0.3741
0:03147
...
0.03134 0:03123 0.03112 0.03102 0.03092 0.03083 0.03062 0.03043 0.03026 0.03010 0.02996 0.02983 0.02971 0.02960
.... 0.2879 .... 0.2349 ....
0.2017 0.1771 0.1589 0.1445 0.1331 0.1129 0 * 0998 0.0908 0.0864 0.0791 0.0756 0.0728 0.0704
h 161.7 160.5 158.2 154.9 148.4
... ... ... ..*
El
f/P
5.913 2.899 1.894 1.386 1.085 0.8830 0.7366 0.6253 0.5408 0.4707 0.4154 0.3657 0.2856 0.03919
0.9828 0.9639 0.9449 0.9266 0.9081 0.8897 0.8708 0.8535 0.8351 0.8160 0.7992 0.7816 0.7461 0.6907
0.03852
0.5672
....
....
0
...
... ... 6.68 ... ...
...
7.10
... ...
7.60
....
0:03329
....
.... 0.0081 .... .... .... 0.0045 .... 0.0003 ....
0.03311
-0,0033
9.58
-0.0066
l0.'25
-0.0094
-
0:03294 0.03277 0.03262 0.03241 0.03233 0.03202 0.03175 0.03151 0.03129 0.03109 0.03093 0.03076 0.03064
....
100' f/P 0.9761 0.9516 0.9274 0.9001 0.8743 0.8491 0.8247 0.7688
....
F.
h 174.4 173.2 171.4 169.2 166.3 162.8 158.7 27.15
_.
130' F.
8
0.3958 0.3624 0.3414 0.3254 0.3118 ~. 0.2988 0.2871 0.05041
..... .....
0.4171 0,3849 0,3652 0.3505 0.3381 0.3271 0.3175 0.3084 0.2999 0.2908
0:70k8 ..., 0.5420
48:34
0:08596
47:QS
,..
0:06424
47.'45
o.'Oiiia
~
26:99
0.04903
0:03584
26:91
0.04775
.....
0:03554
.....
0.3523
26:bO
..... 0.04538 .....
0.2822 0.2481 0.2222 0.2032 0.1862 0.1578 0.1398 0.1272 0.1177 0.1107 0.1053 0.1014 0.0983-
..... .....
26.'iS
0.04318
26184 27.00 27.22 27.68 28.02
0.04113 0.03874 0.03650 0.03439 0.03240
28:84
0.02870
:
0.02528
29 80
8
0.4402 0.4070 0.3875 0.3732 0.3614 0.3507 0.3426 0.3344 0.3269 0.3198 0.3129 0.3058 0.2893 0.12292
....
...
....
0 :i
ik 0:i i 3 ~ o:iiOos
-
h 214.3 213.2 211.9 210.4 208.8 207.1 205.4 203.9 202.3 200.5 198.9 197.2 193.3 188.5 182.2 172.1 101.3 99.40
.....
.....
.....
....
o:Oi498 0.03474 0.03452 0.03430 0.03410 0.03363 0.03325 0.03291 0.03261 0.03232 0.03207 0.03184 0.03164
U
f/P
6.224 3.058 2.002 1.471 1.155 0.9424 0.7896 0.6734 0.5863 0.5146 0.4559 0.4051 0.3305 0.2720 0.2216 0.1701
0.9859 0.9703 0.9533 0.9372 0.9212 0.9036 0,8884 0,8722 0.8567 0.8400 0.8244 0.8091 0.7759 0.7457 0.7144 0.6831
0: 04354
0.5861 0: ii44i 0.5177 0.4656 95:51 0 : i5624 0.4253 0.3919 93 35 o i50e.a 0.3331 91.59 0.14513 0.2981 0.14060 90.40 0.2708 0.13668 89.57 0.2513 0.13318 88.99 0.2357 0.2243 88:iQ 0 : ii703 0.2157 0.2078 0 : iiim 88: io lb.; f fugacity, lb. per sq. in.; h =
0.04241 0.04109 0.04006 0.03945 0.03819 0.10645 0.10331 0.03724 0.10049 0.03652 0.03593 0.09791 0.03540 0:09i35 0.03491 0,03448 0.03412 0:08935 specific volume, CU. f t . per
....
:
-
-
187.3 186.1 184.4 182.8 180.6 178.4 176.1 174.0 171.4 167.5
0.5269
... ...
1
0.9800 0.9579 0.9364 0.9158 0.8933 0.8728 0.8519 0.8338 0.8129 0.7904
... ...
.... 0.4060 .... 0.3308 ....
h
5.610 2.740 1.781 1.298 1.0144 0.8224 0.6826 0.5744 0.4905 0.4200
0.6315
....
f/w. ..
0
.... 0.4457 ....
0.3799 0,3345 0.3002 0.2718 0,2504 0.2131 0.1886 0.1699 0.1580 0.1488 0.1418 0.1363 0.1317
190° F.
...
:
....
....
h 200.4 199.3 197.8 196.3 194.8 193.0 191.2 189.3 187.4 185.4 183.0 180.7 172.9 71.27
0:03795 0.4853 6 9 : 49 0.03746 0.4273 0.03703 0.3821 68:33 0.3484 0.03665 0.3212 0.03629 67:56 0.2731 0.03554 66.97 0.2406 0.03495 66.66 0.2188 0.03447 66.53 0.03407 0.2029 66.53 0.03667 0.1903 0.03334 0.1812 66 83 0.03303 0.1742 0.03275 0.1677 67: 39 p pressure, lb. per sq. in. absolute; D B. t. u. per lb. per O F. abs.
0:&347
0.0100
8.30
...
.... ....
.... .... 0,0109 ....
6.66
....
5.307 2.578 1.664 1.208 0.9332 0.7494 0.6118 0.03368
.... .... ....
... 6.65 ...
l6Oo F. Pa 25 50 75 100 125 150 175 200 225 250 275 300 350 400 450 500 550 600 700 800 900 1000 1250 1500 1750 2000 2250 2500 2750 3000
8
0.3715 0.3388 0.3175 0.3001 0.2809
8
0.4607 0.4280 0.4086 0.3945 0.3825 0.3724 0.3636 0.3558 0.3490 0.3427 0.3362 0.3303 0.3190 0.3078 0.2951 0.2770
c
6.531 3.217 2.107 1.558 1.222 1.000 0.8422 0.7215 0.6309 0.5556 0.4931 0.4420 0.3641 0.3024 0.2528 0.2156 0.1807 0.1447
.... .... ....
*..
47.'io
:
....
.... o:oi83~
46 90 46.81 46.87 47.03 47.26
0:07588 0.07306 0.07051 0.06816 0.06595
47: 87
o:o6in
48:24
0: 05821
220° F. f/P 0.9884 0.9761 0.9620 0.9473 0.9332 0.9174 0.9055 0.8904 0.8769 0.8632 0.8492 0.8363 0.8089 0.7821 0.7575 0.7312
.... .... .... .... ....
h 228.4 227.4 226.1 224.6 223.2 221.6 220.1 218.6 217.0 215.5 214.0 202.3 209.4 206.4 203.2 199.8 195.7 190.0
... ...
8
0.4813 0.4488 0.4293 0.4148 0.4031 0.3932 0.3844 0.3767 0.3697 0.3632 0.3572 0.3517 0.3421 0,3335 0.3257 0.3176 0.3086 0.2980
.... ....
.... .... 134:i3 o:iiia 0.0423 0.408 ,... 0.0406 0.362 124 :45 0.1922 0.0395 0.328 ... .... 0.0386 0.305 120.18 0.1807 0.0377 0.288 .. .. 0.0370 117:io 0.275 0.1713 0.0364 0.265 0.0358 116.. 50 0.255 0.1644 heat content, B. t. u. per lb.; (I = entropy,
....
TABLE11. PHYSICAL AND THERMAL PROPERTIES OF PROPANE found possible to commence recording temperatures about 10 SATURATED LIQUIDAND SATURATED GAS seconds after the pressure was changed. A chronograph was used to record the lapse of time. The record of the change in tem-SATURAT~D GAS--SATURAT~D LIQUIDperature as a function of time was continued for about 120 seconds. U 8 0 P t4 h h 6 f/v In the case of hydrocarbons more viscous than kerosene the effect 125 69.4 0.8388 147.7 0.2799 0.03185 6.2 0.0123 0:8555 of convection currents was so small that cooling curve methods 150 82.3 0.6936 151.2 0.2800 0.03260 14.8 0.0287 0.8357 175 93.8 0.5922 154.2 0.2801 0.03333 22.7 0.0428 0.8182 were unnecessary, since the maximum (or minimum) tem erature 200 104.3 0.5152 156.8 0.2802 0.03403 30.2 0.0556 0.8039 reached by the liquid could be measured easily before a ciange in 225 113.8 0.4535 158.9 0.2803 0.03471 36.9 0.0671 0.7913 temperature due to diffusion occurred. 250 122.4 0.4050 160.8 0.2801 0,03535 42.9 0.0776 0.7803 275 300 325 350 375 400 425 450 475 500 525 550 575 600 625 a
130.6 0.3648 138.1 0.3278 145.3 0.2973 152.1 0.2704 158.6 0.2460 164.8 0.2242 170.5 0.2039 175.9 0.1856 180.9 0.1692 185.8 0.1545 190.6 0.1402 195.1 0.1281 199.6 0.1176 204.1 0.1041 208.5 0.0896 1 temperature, O
-
162 3 0 2796 163:s 0:2789 164.4 0.2779 165.0 0.2768 165.3 0.2752 165.5 0.2739 165.5 0.2724 165.3 0.2707 165.0 0.2690 164.5 0.2672 163.9 0.2652 163.2 0.2631 162.5 0.2609 161 0.258 158 0.253 F; other units
0 03601 48.9 0:03668 54.3 0.03743 59.7 0.03822 65.1 0.03907 70.3 0,03997 75.5 0.04089 80.7 0.04191 86.0 0.04296 91.2 0.04415 97.1 0.04556 103.1 0.04713 109.2 0.04905 116.2 0.05183 123.6 0.05577 133 as in Table I.
0.0871 0.7698 0.0960 0.7590 0.1048 0.7483 0.1131 0.7379 0.1216 0.7263 . .. 0.1300 0.7160 0.1380 0.7057 0.1461 0.6962 0.1542 0.6857 0.1624 0.6793 0.1714 0.6708 0.1800 0.6635 0.1873 0.6555 0.201 0.6471 0.639 0.214
sensitivity, low-resistance galvanometer in connection with a calibrated potentiometer was used to measure the tem erature change due to the adiabatic change in pressure. As tge walls remained a t substantially the same temperature, the cooling curve method had to be employed in order to arrive a t the true adiabatic temperature change. After a little experience it was
The value of the thermocouple voltage at zero time yielded, from calibration of the thermocouple, the change in temperature of the liquid for a known change in pressure. From these data a mean value of (6T/6p). could be obtained for the average pressure existing.2 This measurement was then repeated at a lower pressure and another value of the coefficient obtained. By combining these data with the thermal expansion ( 6 ~ / 6 T ) ,according , to the general relation,
the value of the specific heat at constant pressure tained.
* A list of symbols will be found in Table I.
WBB
ob-
November. 1934
INDUSTRIAL AND ENGINEERING CHEMISTRY
1221
average speciiic gravity of the two phases present as a function of temperature. This mean value becomes almost independent of temperature as the critical temperature is approached. A short extrapolation (2" F.) to the critical temperature allows accurate determination of the critical specific gravity. The slopes of the isotherms above the critical temperature a t the critical specific gravity were plotted as a function of temperature and the temperature corresponding to zero slope was determined. The value thus obtained agreed well with that obtained by rounding the saturation curves to meet a t the critical specific gravity. The critical pressure waa determined by extrapolating the vapor pressure curve to the critical temperature. The extrapolation was only 0.2' F., and, as the vapor pressure curve is quite straight in this region, the value is believed to be known to a t least 1.0 pound per square inch. The vapor pressure of propane as a function of temperature is shown in Figure 4. A comparison of the results of previous investigators has been made recentdy by Francis and Robbins (3). The laws of ideal solutions appear to apply with reasonable accuracy to equilibrium relations in petroleum mixtures (4, 6, 10) except for the more volatile component near the critical point for the mixture in question. Other investigators (6, 9) have compiled fugacity charts which have been based upon the law of corresponding states for their construction. The fugacity of propane as a function of pressure for a series of temperatures is shown in Figure 5. The fugacity was calculated from the relation (6):
The deviation (z) from a perfect gas, which equals pv/RT, was plotted against In p . Progressive graphical integration of this curve for each temperature yielded the change in fu-
k. ; and ipecific volume, 0.06896 cubic'foot peipound. The critical specific gravity was determined by plotting the a Specific gravity, as used here,
is defined as the ratio of the weight of a
unit volume of the material at the giyen pressure and temperature to the weight of a unit volume of water at ita maximum density at 1 atmosphere pressure.
gacity (f) as a function of pressure. The fugacity (jo) was assumed equal to the pressure ( p o ) a t 1.47 pounds per square inch (0.1 atmosphere). The fugacity of Propane thus Cablated agrees very well with that computed by the investigators cited above from the law of corresponding states. The
INDUSTRIAL AND ENGINEERING CHEMISTRY
1222
fugacity was considered as being of enough importance in equilibrium calculations to warrant tabulation, which has been done for the saturated liquid and gas, as well as for the condensed and superheated region, in Tables I and 11.
Vol. 26, No. 11
methods used for the construction of the chart shown in Figure 9, including the five variables-pressure, temperature, specific volume, specific heat content, and specific entropy. Since the absolute values of heat content and entropy cannot be calculated from the measurements here presented, it is necessary to give the results in terms of relative values referred to some arbitrarily chosen datum. For most purposes this causes no difficulty since we are mainly interested in differences rather than absolute values. As convenient datum conditions, the entropy and the heat content of the saturated liquid are arbitrarily taken as zero a t the lower temperature limit of the experimental data. At this lowest temperature the change in entropy with pressure can be calculated by use of the general equilibrium equation (1):
(E)
6p T-
= S(T e ) p
This relation could not be used in the two-phase region for a pure substance, such as propane, but was there replaced by the Clapeyron equation: Ah
1
0.03 VOLUME
0.04 CUBIC
0.05
0.06
F E E T PER
POUND
FIGURE7. SPECIFIC VOLUME OF LIQUID PROPANE Figure 6 shows the specific volume of gaseous propane as a function of temperature at constant pressure. In Figure 7 are shown similar curves on a much enlarged volume scale for the condensed region, the point C on the saturated liquid line being the critical point. I n order to obtain the first derivative of these curves, they were plotted on as large a scale as consistent with the accuracy of the data, and the slopes of the curves were measured, thus furnishing the values of (SulST),required for the determination of Cpby the method described above. I n Figure 8 is shown the specific heat of liquid propane at constant pressure as a function of temperature a t a series of pressures. The dotted portions of the curves at the higher temperatures were based upon extrapolated values of (6u/ST),. This extrapolation was necessary because the pressure-volume-temperature data were determined only to 220' F., and measurement of slopes at the ends of experimental curves in the critical region was unsatisfactory. The specific heat at the lower temperatures (below 190" F.) is believed to be accurate to about 1.5 per cent. Each of the points shown is the average of at least six, and for the most part ten, measurements. The average deviation of the individual points from the mean value was about 2 per cent. The value of the specific heat a t the lower temperatures (70" F.) is somewhat higher than would have been expected from the extrapolation of the data of other investigators (2). However, since extrapolation of specific heat of a liquid under saturation conditions near the critical point is somewhat uncertain, the deviation could easily be explained on that basis. From the data presented, the changes in heat-content (also known as total heat and as enthalpy) and entropy which occur upon change of state have been calculated. Of the various graphical methods available for presentation of such information, the temperature-entropy plane furnishes the best picture when both the condensed and superheated regions are included. The following discussion outlines the
dP TAU dT
From the former relation of entropy to pressure at constant temperature the position of a series of constant-pressure and -volume intercepts was determined at the datum temperature, the pressure-volume-temperature data being directly employed to locate the constant-volume intercepts after the constant-pressure points had been determined. As stated above, this procedure was somewhat modified in the twophase region. From the specific heat measurements, the position of a constant-pressure line was determined as a function of temperature by use of the relation:
($), = TCP As one point on this line at the datum temperature was known and its slope was determined by the above relation, it could be readily drawn on the temperature-entropy plane. From
I25
IO0
150
TCUPCRATURE
115
200
Of.
FIGURE8. SPECIFIC HEATAT CONSTANTPRESSURE OF LIQUIDPROPANE the pressure-volume-temperature data the pressure and the volume were known at each temperature along this line, and, by applying the same methods as were used a t the datum temperature, the entire field of constant pressure and volume lines were drawn in. The change in heat content with pressure at constant temperature was determined by graphical integration of the expression : ($)T
= v
- T($)
November, 1934
INDUSTRIAL AND ENGINEERING CHEMISTRY
1223
All of the above calc u l a t i o n s could have been carried out by a m a t h e m a t i c a l procedure, but the graphical methods here employed were more expeditious and did much to help in correlating the data a n d i n p o i n t i n g out errors. T h e graphs used in these calculations mere d r a w n t o such a scale that values c o u l d be r e a d off within a n a c c u r a c y comparable to that of the experimental measurements. The results of these calculations for t h e s a t u r a t e d liquid and gas are presented in Table I, along with the specific volume and the ratio of the fugacity to pressure, which is the same for both the saturated liquid and gas. S i m i l a r data for the condensed a n d t h e s u p e r h e a t e d regions a r e reported in Table 11. In the condensed region both the entropy and the heat content were carried at least one place farther than was warranted by the I specific heat measure ments. This was done B.T.U. PER LB. PER O F . to allow the more acI I 0.10 0.20 0 30 0.40 curate evaluation of the isothermal changes i n FIGURE 9. TEMPERATURE-ENTROPY CHARTFOR PROPANE these properties which By following the same are known much more precisely than the change with temperamethod as o u t l i n e d ture. The changes in heat content and entropy a t low presabove, a field of con- sure (25 pounds per square inch) agree very well with those SATURATED GAS stant-pressure l i n e s calculated from specific heat measurements made by other was drawn on the heat investigators ( 7 ) a t atmospheric pressure. In Figure 10 are content-temperashown the deviations of the tabulated heat contents of the t u r e p l a n e . There saturated liquid and gas from those obtained by Dana and was no need of including the constantrvolu m e l i n e s on t h i s a u x i l i a r y p l a n e as t h e y were a l r e a d y 1 fixed on the t e m I 1 I 1 70 80 90 110 120 p e r a t ure-e n t r o p y T E M P E R A T 2 OF. plane. The relation, FIQURE 10. DEVIATIONS OF HEAT CONTENT VALUESFROM THOSEOBTAINED IN LINDELABORATORIES ( $ , ) p = T ( g ) =C,
G=Gl
was used to establish one constant-pressure line as a function of temperature from the specific heat determinations. From t h e temperature us. heat content plane, the temperatures a t which lines of constant heat content intersected those of contitant pressure were determined, and the lines of constant heat content were transferred to the temperature-entropy plane,
40 80 T E M P E R AT U R E
I20
160
200
DLGRE E 5 F A H R E N H E I T
FIGURE 11. HEATOF VAPORIZATION OF PROPANE
INDUSTRIAL AND ENGINEERING
1224
his co-workers (3) of the Linde Laboratories. The deviations were calculated by taking the heat content of the saturated liquid a t 60” F. of both sets of data equal. The values obtained by the present authors were then subtracted from the Linde values to give the deviations plotted. The lower values reported by the other observers for the saturated liquid are due to their lower extrapolated values of specific heat. The much larger deviation of the heat content of the saturated gas is due to the divergence of the latent heats of vaporization as indicated in Figure 11. The values obtained a t the Linde Laboratories were directly measured and indicate a somewhat higher value for the latent heat than was obtained by application of the Clapeyron equation to the data reported here. Since the Linde data were extrapolated some distance in order to obtain their reported values a t the upper end of their temperature range (125” F.), the agreement is considered satisfactory. ACKNOWLEDGMENT The results here reported were obtained as part of the work of Research Project 37 of the American Petroleum Institute.
CHEMISTRY
Vol. 26, No. 11
Thanks are due to the institute for encouragement and financial assistance.
LITERATURE CITED (1) Bur. Standards, Circ. 279 (1925). (2) Dana, L. I., Jenkins, A. C., Burdick, J. N., and Timm, R. C., Refrigerating Eng., 12, 387 (1926). (3) Francis, A. W.,and Robbins, G. W., J. Am. Chem. SOC.,55, 4339 (1933). (4) Lacey, W. N., Proc. Calif. Natural Gasoline Assoc., 9, 2 (Jan. 5, 1934). (6) Lewis, G. N., and Randall, M., “Thermodynamics,” pp. 132-40, 192, McGraw-Hill Book Co.,New York, 1923. (6) Lewis, W.K., and Kay, W. C., OiE Gas J . , 32, No. 45,40 (1934). (7) Lewis, W.K., and McAdams, W. H., Chem. & Met. E w . , 36, 336 (1929). (8) Sage, B. H., and Lacey, W. N., IND. ENQ. CHEM.,26, 103 (1934). (9) Selheimkr, C. W., Souders, M., Jr., Smith, R. L., and Brown, G. G., Ibid., 24, 515 (1932). (10) Souders, M., Jr., Selheimer, C. W., and Brown, G. G., Ibid.,24, 517 (1932). R ~ C E I V EJuly D 11, 1934.
Composition of Potash Fertilizer Salts for Sale on the American Market J. W. TURRENTINE, Bureau of Chemistry and Soils, Washington, D. C.
I
N RESPONSE t o current demand for more detailed in-
formation concerning the composition of fertilizer potash salts than that represented by a mere statement of potash content, there have been assembled the following complete analyses of potash salts, domestic and foreign, now being offered for sale on the American market. Without exception, these analyses have been provided through the courtesy and collaboration of the respective producers and importers. It is common knowledge that the market price of agricul-
tural potash salts is determined by the actual potash (KzO) content. The sulfate commands a higher price than the chloride; otherwise, little attention is paid to the incidental constituents with the exception of magnesium salts-for example, a prominent constituent of the imported “sulfate of potashmagnesia.” Accordingly, as between assignments, the incidental ingredients may vary over considerable ranges as illustrated by some of the tables here presented. A much greater variation is possible in the low-analysis than in the high-analysis products.
SALTSOF DOMESTIC ORIGIN TABLEI. POTASH 1. HIGH-ANALYSISMURIATEPRODUCED BY THE AMERICANPOTASE & CHEMICAL CORP. (WORKSAT TRONA,CALIF.; SALESOFFICE,70 PINEST., NEW YORK);ORIOIN,BRINEFROM SALINIB LAKE TRONA MURIATE (AQRICULTURAL GRADE)
% Potash (&O) Potassium chloride actual Potsssium chloride: equivalent” Sodium chloride Potassium bromide
%
61.3
95.8 97.1 1.4 1.96
Potassium iodide Sodium tetraborate Sodium carbonate Sodium sulfate Moisture
0.002 0.3 0.3 Trace 0.2
u.
POTASH 8 A L T S b PRODUCED BY s.POTASH CO. (PLANT NEAR CARLSBAD, N. Msx.; SALES OFFICE,342 MADISON Avs., NEW YORK); ORIQIN,MINES OF SALINEMINERALS (SYLVINITE)
2.
-HIOH-ANALYSIS
MURIATE--
MANURE
SALTS (26% MINIMUM)
% Potash (KtO) 62.4 Potassium chloride 9s. 7 Sodium chloride 1.2 Caloium, magnesium. and NHaOH
0.1
SuRk
Trace Trace Trace
Insol. matter Moisture
K10
% Potas! (KO) Potassium chloride Sodium chloride Sodium sulfate Caloium sulfate Magnesium sulfate Magnesium chloride Boric oxide (Blot) Inaol. matter Moisture
28.3 44.7 53.2 None 0.7 0.4 0.2 0.028 0.7 0.1
3. LOW-ANALYSIS MUBIATE~ PRODUCEID BY POTASH Co. OF AMERICA (PLANT NEAR CARLSBAD, N. Mix.; SALESOFFICE,1012 M ~ C A N T I LTRUST E BLDG., BALTIMORB) : ORIGIN.MINESOF SALINEMINERALS(SYLVINITE) c
POTASH (MANURE) SALTS
Potaah (K:O) Potassium chloride Sodium chloride Magnesium ohloride
92 27.6-34.5 43.6-54.6 43.8-63.1 0.4
._
-
Calcium aulfate Aluminum sulfate Moisture I ~ o l matter .
% 0.62.8 0.3 0.6
0.6-1.2
POTASH SALTSPRODUCED BY U. S. INDUSTRIAL CHEMICAL Co. (PLANTAT BALTIMORE. SALESOFFICE.A. L. WEBB & SONS. 206 NATIONALM A R I N ~ BANK B L D ~BALTIMORE).ORIGIN THE INCINERATED PRODUCT FROM EVAPCIRATED’DISTILLERY WASTE (TI& MINERALCONTENTOF CANEMoLASSES), HENCETHE TRADENAMB. VEGETABLE POTASH” 4.
-LOW-ANALYSIS
SALTSd
-
Potash (KgO), sol. in dil. HCl Potaeh KtO), sol. in water Lime ( d a o ) Sulfur (as 608) Chlorides (as C1 Carbonates &Or) Iron and aluminum oxides Magnesia, (MgO) Phosphoric acid (PrOr), citrate sol. Nitrogen Inaol. matter Moisture (at 100’ C.)
(e
%
34.7 33.9 16.1 12.5 8.9
5.1 6.4 4.8 1.7 0.3 5.8 0.2
-HIGH-ANALYSIB
SALT-
Potash (KpO) Chlorides (Cl) Sulfates (sod) Total Moisture sol. matter Total insol. matter
% 56.1 28.6 15.4 2.8 99.7 0.3
SULFATEOF POTASHPRODCCED B Y KORTHAMERICAN CEIMENT Co. (WOUKSAT HAQBRSTOWN. MD.:SALESOFFICE.BALTIMORE TRUETBLDO.,
5.
BALTIXORE);ORIGIN.PPTD. F u m
c
FROM CEMBNT POTASH’
CEIMENTKILNS
%
%
Potash KzO) 20;s Alumina (AlrOs) 3: 4 Lime ( d a 0 ) (water sol., 7.42%) 28.3 Soda (NatO) 1.3 Sulfur SO;) 29.8 Magnesia ( M t 0) 1.2 9.6 CarEonated 2.8 Silica (hot) 2.1 Moisture 0.2 Iron (FeaOa) 5 This item varies a t times between about 9698% while. minor opnstituents remain approximately constant; it includes the potassium bromide calculated to potasaum chloride. b Analvsea bv Hockatadbr Laboratories. Analyoem b% Gaacoyne and Co. d Compoaita sample representing 100 carloads; from ”Potaah.” by J. W. Turrentine, p. 129,John Wiley & SOM,New York, 1926. Landolt, P. E., Chem. & Md. Eng., 40,346 (1933).
(cor)
